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单词 Cycle notation
释义

Cycle notation

中文百科

置换 Permutation

(重定向自Cycle notation)
P(3,3)=6
(2,5,1,4,3,6)的置换图

排列英语:Permutation)是将相异对象或符号根据确定的顺序重排。每个顺序都称作一个排列。例如,从一到六的数字有720种排列,对应于由这些数字组成的所有不重复亦不阙漏的串行,例如"4, 5, 6, 1, 2, 3" 与1, 3, 5, 2, 4, 6

置换的广义概念在不同语境下有不同的形式定义:

英语百科

Permutation 置换

(重定向自Cycle notation)
Each of the six rows is a different permutation of three distinct balls
In the popular puzzle Rubik's cube invented in 1974 by Ernő Rubik, each turn of the puzzle faces creates a permutation of the surface colors.
Permutations of multisets
Composition of permutations corresponds to multiplication of permutation matrices.

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). These are all the possible orderings of this three element set. As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters. The study of permutations of finite sets is a topic in the field of combinatorics.

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更新时间:2025/6/17 22:27:04